Hi,
The only inspection required would be UDP.
I would assume that the first packet is allowed to pass?
packet-tracer input inside udp <vlan_ip> 67 <server_ip> 67
You could also make a capture to see were the packets get dropped (first on ingress interface and then on egrees interface).
You could use the following command to troubleshoot:
show asp drop
capture asp-drop type asp-drop all
Additionally, you could manually allow (on both interfaces of ASA) traffic on UDP 67 between the DHCP relay (Vlan IP interface towrds the clients) and the DHCP Server.
Traian